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Question

A solid toy in the form of a hemisphere surmounted by a right circular cone.Height of the cone is 2 cm and the diameter of the base is 4 cm.if a right circular cylinder circumstances the toy,find how much more space it will cover

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Solution

Solution:

Given that,

Radius of the cone, cylinder and hemisphere (r) = 2 cm

Height of the cone (l) = 2 cm

Height of the cylinder (h) = 4 cm

Volume of the cylinder ,V1=πr2h=π×22×4=16π cm3……… (1)

Volume of the cone ,V2=13πr2L=13π×22×2=83π cm3 ………. (2)

Volume of the hemisphere ,V3=23π×23=16π3 cm3 ………. (3)

So, remaining volume of the cylinder when the toy is inserted to it = V1 – (V2 + V3)

V = 16π – 8 π = 8 π cm3

Hence, remaining volume of the cylinder when toy is inserted into it = V = 8π cm3


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